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Improved precise integration method for differential Riccati equation

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Abstract

An improved precise integration method (IPIM) for solving the differential Riccati equation (DRE) is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method (PIM) for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples show that the IPIM is stable and gives the machine accuracy solutions.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian, 116024, Liaoning Province, P. R. China

    Qiang Gao  (高 强), Wan-xie Zhong  (钟万勰) & Hong-wu Zhang  (张洪武)

  2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, 116024, Liaoning Province, P. R. China

    Shu-jun Tan  (谭述君)

Authors
  1. Qiang Gao  (高 强)
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  2. Shu-jun Tan  (谭述君)
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  3. Wan-xie Zhong  (钟万勰)
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  4. Hong-wu Zhang  (张洪武)
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Additional information

Project supported by the National Natural Science Foundation of China (Nos. 10902020 and 10721062)

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Gao, Q., Tan, Sj., Zhong, Wx. et al. Improved precise integration method for differential Riccati equation. Appl. Math. Mech.-Engl. Ed. 34, 1–14 (2013). https://doi.org/10.1007/s10483-013-1648-8

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  • DOI: https://doi.org/10.1007/s10483-013-1648-8

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Chinese Library Classification

2010 Mathematics Subject Classification

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